#include <Eigen/Dense>
#include <iostream>

using namespace std;
using namespace Eigen;

int
main()
{
	MatrixXd A = MatrixXd::Random(100, 100);
	MatrixXd b = MatrixXd::Random(100, 50);
	MatrixXd x = A.fullPivLu().solve(b);
	double relative_error = (A * x - b).norm() / b.norm(); // norm() is L2 norm
	cout << "The relative error is:\n" << relative_error << endl;
}
